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We report a measurement of the ratios of branching fractions R(D, where denotes an electron or a muon. The results are based on a data sample containing 772 × 10 6 B B events recorded at the Υ(4S) resonance with the Belle detector at the KEKB e + e − collider. The tag-side B meson is reconstructed in a semileptonic decay mode, and the signal-side τ is reconstructed in a purely leptonic decay. The results are R(D) = 0.307 ± 0.037 ± 0.016 and R(D * ) = 0.283 ± 0.018 ± 0.014, where the first uncertainties are statistical and the second are systematic. These results are in agreement with the Standard Model predictions within 0.2 and 1.1 standard deviations, respectively.